Is service tax paid on gta availed against excise duty

yes

But Service Tax Paid Must Be In Cash( Not Utilise Any Cenvat Credit)

And Service Tax  on GTA Paid It Taken AS a Credit -Credit

Yes, undoubtly you had paid the ST through challan and same is eligible input as per Rule 3(1)(x) and respectively EC as per Rule 3(1)(xi) and SHEC as per Rule 3(1)(xii).

Please note

1.EC Credit on Taxable service can only be utilised for EC(Escise) on Final Product or EC (ST) on output sevices.

2.SHEC Credit on Taxable service can only be utilised for SHEC(Escise) on Final Product or SHEC (ST) on output sevices.

3.Service Tax Credit can be utilised for any purpose other than ADD (Health cess) or Clean energy Cess.

Regards

Karan